Exact calculation of the tip friction within the harmonic model

In this paper we consider some general issues related to the calculation of energy dissipation in the non-contact atomic force microscopy (NC-AFM) systems due to friction force mechanism. First of all, we show how the classical friction coefficient due to the tip–surface force autocorrelation function can be calculated exactly by retaining an arbitrary number of terms in the expansion of the force in atomic displacements. Secondly, using the exact expansion we confirm our previous findings [J. Phys.: Condens. Matter 14 (2002) 4329] that the local surface phonons and their anharmonicity play a crucial role in the dissipation processes. Finally, we illustrate the method on a calculation of the friction coefficient and the dissipation energy for a simple analytically solvable model of the NC-AFM system.